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CBSE Class 10 Mathematics Basic Sample Paper 22 2027 Solutions

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SAMPLE PAPER 22 Sample Paper 22 Class - 10th Exam - 2026 - 27 Mathematics - Basic Time : 3 Hours Max. Marks : 80 General Instructions : Read the following instructions carefully and follow them: 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B,… — Page 1 of 13

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page 298 Cbse Class 10th Mathematics - Basic SP Thus (b) is correct option. 4. Which of the following equations has the sum of its roots as 3 ? (a) x x 2 3 6 0 2 − + = (b) x x 3 3 0 2 − + − = (c) x x 2 2 3 1 0 2 − + = (d) x x 3 3 3 0 2 − + = AAns : ] Sum of the roots, α β + Coefficient of… — Page 2 of 13

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SAMPLE PAPER 22 Then, AB . m 20 5 = DC = and EC BE BC = − BE AD = − . 22 1 5 = − . m 20 5 = [BC AD = ] Let θ be the angle of elevation make by observer’s eye to the top of the tower i.e. DCE + , tanθ B P = DC CE = . . 20 5 20 5 = tanθ 1 = tanθ tan45 = c & θ 45 = c Thus (b) is correct option. 9.… — Page 3 of 13

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page 300 Cbse Class 10th Mathematics - Basic SP AAns : Let radius of circle be r and side of a square be a. According to the given condition, Perimeter of a circle Perimeter of a square = r 2π a 4 = a r 2 π = ...(1) Now, Area of square Area of circle a r 2 2 π = ^ h r r 2 2 2 π π = ^ h [from Eq.… — Page 4 of 13

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SAMPLE PAPER 22 and a2 , , b k c 12 2 2 2 = = =− The equation for no solution if a a 2 1 b b c c 2 1 2 1 ! = or, k 12 k 3 2 1 ! = − − From k 12 k 3 = we have k k 36 6 2 & ! = From k 3 2 1 ! - - we have k 6 ! Thus k 6 =− Thus (a) is correct option. 18. The quadratic equation x x 3 2 2 0 2 + + = has… — Page 5 of 13

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page 302 Cbse Class 10th Mathematics - Basic SP OD OA OB OC = Due to the vertically opposite angles, AOD + COB + = Thus by SAS similarity we have AOD T ~ COB T Thus A C + + = and . B D + + = because of corresponding angles of similar triangles. 22. Find the value of º º º º sin cos cos sin 30 60 30… — Page 6 of 13

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SAMPLE PAPER 22 OC OA OD BO = x x 3 5 + + x x 2 1 = − − x x 5 2 + − ^ ^h h x x 1 3 = − + ^ ^h h x x x 2 5 10 2 − + − x x x 3 3 2 = + − − x x 3 10 2 + − x x 2 3 2 = + − x 3 10 - x 2 3 = − x x 3 2 - 10 3 = − & x 7 = Thus x 7 = . 25. In figure, a circle touches all the four sides of a quadrilateral… — Page 7 of 13

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page 304 Cbse Class 10th Mathematics - Basic SP y 5 4 2 3 2 5 = − = y 2 5 5 2 1 # = = Hence x 2 1 = and y 2 1 = . 28. In the given figure, P and Q are the points on the sides AB and AC respectively of , ABC T such that . AP 3 5 = cm, PB 7 = cm, AQ 3 = cm and QC 6 = cm. If . PQ 4 5 = cm, find . BC… — Page 8 of 13

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SAMPLE PAPER 22 Radius of cylinder 2 12 6 = = cm Volume of water displaced in cylinder will be equal to the volume of sphere. ( ) h 6 2 π ( ) 3 4 3 3 π = h 6 6 # # 3 4 3 3 3 # # # = h 6 6 # # 4 3 3 # # = h 6 6 4 3 3 1 # # # = = cm Hence the water level rises is 1 cm. O A hemispherical tank, of… — Page 9 of 13

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page 306 Cbse Class 10th Mathematics - Basic SP and y m m m y m y 1 2 1 2 2 2 = + + 2 3 2 1 3 6 # = + − + − ^ ^ h h 5 2 18 = − − 5 20 4 = − =− Hence, coordinates of point A is ,2 4 - ^ h. Since point A also lies on the line x k y 3 1 0 + + = ^ h , its coordinates must satisfies this line. Thus k 3… — Page 10 of 13

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SAMPLE PAPER 22 C.I. xi fi u h x a i i = − f u i i 40-44 42 4 -3 -12 44-48 46 6 -2 -12 48-52 50 10 -1 -10 52-56 54 a = 14 0 0 56-60 58 10 1 10 60-64 62 8 2 16 64-68 66 6 3 18 68-72 70 2 4 8 f 60 i = / f u 18 i i = / Let a be assumed mean where a 54 = Mean, M a f f u h i i i # = + / / . 54 60 18 4… — Page 11 of 13

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page 308 Cbse Class 10th Mathematics - Basic SP the sides are x 20 2 - and x 30 2 - . ( ) V x ( )( ) x x x 20 2 30 2 = − − ( ) x x x 4 100 600 = − + 2 ( ) V x x x x 4 100 600 = − + 3 2 (ii) Here we have to find ( ) V 6 using the remainder theorem. We divide ( ) V x x x x 4 100 600 = − + 3 2 by x 6… — Page 12 of 13

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SAMPLE PAPER 22 38. Mr. RK Agrawal is owner of a famous amusement park in Delhi. The ticket charge for the park is Rs 150 for children and Rs 400 for adult. Generally he does not go to park and it is managed by team of staff. One day Mr Agrawal decided to random check the park and went there. When… — Page 13 of 13

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